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30 Jul 2018, 00:51
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Difficulty:

45% (medium)

Question Stats:

65% (02:22) correct 35% (02:22) wrong based on 23 sessions

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Amy deposited $1,000 into an account that earns 8% annual interest compounded every 6 months. Bob deposited$1,000 into an account that earns 8% annual interest compounded quarterly.

If neither Amy nor Bob makes any additional deposits or withdrawals, in 6 months how much more money will Bob have in his account than will Amy have in hers?

(A) $40 (B)$8
(C) $4 (D)$0.40
(E) $0.04 _________________ Math Expert Joined: 02 Aug 2009 Posts: 6501 Re: Amy deposited$1,000 into an account that earns 8% annual interest com  [#permalink]

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30 Jul 2018, 03:08
Bunuel wrote:
Amy deposited $1,000 into an account that earns 8% annual interest compounded every 6 months. Bob deposited$1,000 into an account that earns 8% annual interest compounded quarterly.

If neither Amy nor Bob makes any additional deposits or withdrawals, in 6 months how much more money will Bob have in his account than will Amy have in hers?

(A) $40 (B)$8
(C) $4 (D)$0.40
(E) $0.04 When compounded semiannually, time gets doubled and rate halted If compounded quarterly, time gets four times and rate 1/4th Since we are looking for 6 months.. The one compounded every six months.. t is 1 and r=8/2=4 Amount = 1000(1+4/100)=1000*104/100=1040 The one compounded quarterly.. t=2 and r=8/4=2 Amount =1000(1+2/100}^2=1000*1.02*1.02=1040.4 So excess = 1040.4-1040=$0.40

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Amy deposited $1,000 into an account that earns 8% annual interest com [#permalink] ### Show Tags 30 Jul 2018, 14:07 Bunuel wrote: Amy deposited$1,000 into an account that earns 8% annual interest compounded every 6 months.
Bob deposited $1,000 into an account that earns 8% annual interest compounded quarterly. If neither Amy nor Bob makes any additional deposits or withdrawals, in 6 months how much more money will Bob have in his account than will Amy have in hers? (A)$40
(B) $8 (C)$4
(D) $0.40 (E)$0.04

Amy - interest only
Every 6 months, Amy's interest is paid at the annual 8% rate divided by 2 (rate/# of compounding periods).

Every six months she earns $$\frac{.08}{2}=.04$$ on her account balance (principal + any accrued interest)

At the 6-month mark, Amy gets her first interest payment of 4% (on $1,000). Amy's INTEREST EARNED at 6 months: $$(.04 * 1,000)= 40$$ Bob - interest only Every 3 months, Bob's interest is paid at the annual 8% rate divided by 4 (rate/# of compounding periods). Every 3 months, he earns $$\frac{.08}{4}=.02$$ interest on his accumulated balance 1) After 3 months he gets paid $$(.02 * 1,000) = 20$$ Now Bob has $$1,020$$ 2) At the 6-month mark, he gets paid $$(.02 * 1,020) = 20.40$$ Bob's INTEREST EARNED after six months: $$(20 + 20.40) = 40.40$$ Difference between Amy and Bob? $$40.40 - 40.00 = 0.40$$ Answer D Compound interest formula: $$A= P(1+\frac{r}{n})^{nt}$$ A = total amount, P = principal, r = annual interest rate in decimal form, n = number of interest payments in a year, and t = time in years Amy - 8% annual compounded every 6 months In half a year: $$A= 1,000(1+\frac{.08}{2})^{(2*\frac{1}{2})}$$ $$A=1,000(1.04)^1=(1,000*1.04) = 1,040$$ After six months, Amy's total is $$1,040$$ Bob - 8% annual compounded quarterly In half a year, i.e., two quarters $$A=1,000(1+\frac{.08}{4})^{(4*\frac{1}{2})}$$ $$A=1,000(1.02)^2$$ $$1.02*1.02=1.0404$$ After 6 months Bob has $$(1.0404 * 1,000)=1,040.40$$ Difference? $$1,040.40 - 1,040.00 = 0.40$$ Answer D _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Amy deposited$1,000 into an account that earns 8% annual interest com &nbs [#permalink] 30 Jul 2018, 14:07
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